Polynomial Long Division Concepts

The video tutorial explains how to solve a polynomial division problem using long division. It begins with setting up the problem and rewriting it in long division form. The process is broken down into four main steps: dividing the leading variables, multiplying and distributing, subtracting and combining like terms, and repeating the process until reaching the remainder. The tutorial concludes with writing the final answer, including the remainder over the original divisor.

What is the first step in solving the polynomial division problem?

• Multiply the divisor by the dividend

• Rewrite the problem in long division form

• Add the exponents of the variables

• Subtract the divisor from the dividend

In the long division setup, where is the divisor placed?

• Inside the division sign

• Outside the division sign

• Above the division sign

• Below the division sign

What is the leading variable inside the dividend?

• x

• 3x

• 24

• x squared

How do you determine the exponent when dividing variables?

• Divide the exponents

• Subtract the exponents

• Multiply the exponents

• Add the exponents

Where should the result of x squared divided by x be placed?

• Over the x squared

• Over the negative 3x

• In a new placeholder

• Over the negative 24

What is the next step after dividing the leading variables?

• Multiply the result by the divisor

• Subtract the result from the divisor

• Add the result to the dividend

• Divide the result by the divisor

What is the result of multiplying x by (x - 7)?

• x squared + 7x

• x squared - 7x

• x - 7

• x squared + x

What should you do after multiplying and distributing?

• Subtract the new expression from the dividend

• Divide the new expression by the divisor

• Add the new expression to the dividend

• Multiply the new expression by the divisor

What happens to the signs when subtracting the new expression?

• They are halved

• They are doubled

• They are inverted

• They remain the same

What is the result of combining -3x and 7x?

• -4x

• 0

• 4x

• 10x